JAKARTA, April 3 (Reuters) - An Indonesian soldier was shot dead and two separatist rebels killed in clashes with security forces near the giant Grasberg copper mine in Papua operated by Freeport McMoRan Inc, an Indonesian military spokesman said on Tuesday.

A separatist group, however, said that only one of its members had died and that dozens of Indonesian troops were killed in clashes that began on Sunday.

Papua has suffered a simmering separatist conflict since it was incorporated into Indonesia after a widely criticised U.N.-backed referendum in 1969 and foreign media access to parts of the province is often difficult or, at times, restricted.

Papua Military spokesman Muhammad Aidi said the soldier was killed during a joint military and police operation to "reclaim villages controlled by armed criminal separatists".

"It appears (the separatists) were ready for the security forces and so there was a gun fight with the military," Aidi said in a statement.

Six villages were still occupied by separatists and indigenous Papuans after more than 1,000 residents were evacuated in November following a string of shootings, he said.

Drone footage showed two separatists were killed and dozens wounded in the clash, he said. No civilians were hurt, but separatists torched a house, a school and a hospital, said Aidi.

According to the West Papua National Liberation Army (TPNPB), a separatist group, one of its members was shot dead in a clash with Indonesian special forces near Banti village early on Sunday morning.

Hendrikus Uwamang, a spokesman for the group, said at least 28 Indonesian security personnel and several guides were also killed in the clash. Fighting continued on Monday and a 10-year-old boy was also killed, when his house was hit by a shell and caught fire, he said.

Papua Police chief Boy Rafli Amar was quoted in state media last week as saying attacks by "armed criminals" had become more frequent lately near the Grasberg mine. Amar could not be reached for comment on Tuesday.

Members of Indonesia's security forces have been accused by rights activists of abducting and torturing Papuans and using deadly force to quell protests.

TPNPB, which is linked to the Free Papua Movement (OPM), says it is at war with Indonesian authorities and wants to "destroy" Freeport in an effort to gain sovereignty for the region.

President Joko Widodo, after coming to power in 2014, had pledged to speed up development of Papua and ease media restrictions.

But while investment has risen and efforts made to address some human rights concerns, activists say foreign journalists continue to be blocked or face obstacles when trying to report there.

Jakarta is currently in talks with Freeport over ownership of Grasberg, and hopes to gain a majority stake in the world's second-biggest copper mine this month, with the Papua government and a local regency jointly gaining rights to a 10 percent stake. (Reporting by Fergus Jensen and Agustinus Beo Da Costa Editing by Ed Davies and Manolo Serapio Jr.)